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<b>An Object Oriented Finite Element Library</b></font></p>
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<div class="header">
  <div class="summary">
<a href="#pub-methods">Public Member Functions</a> &#124;
<a href="classOFELI_1_1Tetra4-members.html">List of all members</a>  </div>
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<div class="title">Tetra4 Class Reference<div class="ingroups"><a class="el" href="group__OFELI.html">OFELI</a><a class="el" href="group__OFELI.html">OFELI</a> &raquo;  &#124; <a class="el" href="group__Shape.html">Shape Function</a></div></div>  </div>
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<p>Defines a three-dimensional 4-node tetrahedral finite element using <code>P<sub>1</sub></code> interpolation.  
 <a href="classOFELI_1_1Tetra4.html#details">More...</a></p>
<div id="dynsection-0" onclick="return toggleVisibility(this)" class="dynheader closed" style="cursor:pointer;">
  <img id="dynsection-0-trigger" src="closed.png" alt="+"/> Inheritance diagram for Tetra4:</div>
<div id="dynsection-0-summary" class="dynsummary" style="display:block;">
</div>
<div id="dynsection-0-content" class="dyncontent" style="display:none;">
 <div class="center">
  <img src="classOFELI_1_1Tetra4.png" usemap="#Tetra4_map" alt=""/>
  <map id="Tetra4_map" name="Tetra4_map">
<area href="classOFELI_1_1FEShape.html" title="Parent class from which inherit all finite element shape classes. " alt="FEShape" shape="rect" coords="0,0,64,24"/>
</map>
 </div></div>
<table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr class="memitem:afda2840deb189b3ccb3feb1856358935"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="afda2840deb189b3ccb3feb1856358935"></a>
&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classOFELI_1_1Tetra4.html#afda2840deb189b3ccb3feb1856358935">Tetra4</a> ()</td></tr>
<tr class="memdesc:afda2840deb189b3ccb3feb1856358935"><td class="mdescLeft">&#160;</td><td class="mdescRight">Default Constructor. <br /></td></tr>
<tr class="separator:afda2840deb189b3ccb3feb1856358935"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a9be934f7aa82f874efa8abb69f925b8d"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a9be934f7aa82f874efa8abb69f925b8d"></a>
&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classOFELI_1_1Tetra4.html#a9be934f7aa82f874efa8abb69f925b8d">Tetra4</a> (const <a class="el" href="classOFELI_1_1Element.html">Element</a> *el)</td></tr>
<tr class="memdesc:a9be934f7aa82f874efa8abb69f925b8d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Constructor when data of <a class="el" href="classOFELI_1_1Element.html" title="To store and treat finite element geometric information. ">Element</a> <code>el</code> are given. <br /></td></tr>
<tr class="separator:a9be934f7aa82f874efa8abb69f925b8d"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:acf0682cace284156dcbc3f9c45062241"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="acf0682cace284156dcbc3f9c45062241"></a>
&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classOFELI_1_1Tetra4.html#acf0682cace284156dcbc3f9c45062241">~Tetra4</a> ()</td></tr>
<tr class="memdesc:acf0682cace284156dcbc3f9c45062241"><td class="mdescLeft">&#160;</td><td class="mdescRight">Destructor. <br /></td></tr>
<tr class="separator:acf0682cace284156dcbc3f9c45062241"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a578b9f2f623966f955548e89ccce995a"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a578b9f2f623966f955548e89ccce995a"></a>
void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classOFELI_1_1Tetra4.html#a578b9f2f623966f955548e89ccce995a">set</a> (const <a class="el" href="classOFELI_1_1Element.html">Element</a> *el)</td></tr>
<tr class="memdesc:a578b9f2f623966f955548e89ccce995a"><td class="mdescLeft">&#160;</td><td class="mdescRight">Choose element by giving its pointer. <br /></td></tr>
<tr class="separator:a578b9f2f623966f955548e89ccce995a"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a4fc79aaeb587148410021052f410d4dc"><td class="memItemLeft" align="right" valign="top"><a class="el" href="group__Util.html#gaccfeb6b1e8cf41731fde610549bee67c">real_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classOFELI_1_1Tetra4.html#a4fc79aaeb587148410021052f410d4dc">Sh</a> (size_t i, <a class="el" href="structOFELI_1_1Point.html">Point</a>&lt; <a class="el" href="group__Util.html#gaccfeb6b1e8cf41731fde610549bee67c">real_t</a> &gt; s) const </td></tr>
<tr class="memdesc:a4fc79aaeb587148410021052f410d4dc"><td class="mdescLeft">&#160;</td><td class="mdescRight">Calculate shape function of node <code>i</code> at a given point <code>s</code>.  <a href="#a4fc79aaeb587148410021052f410d4dc">More...</a><br /></td></tr>
<tr class="separator:a4fc79aaeb587148410021052f410d4dc"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a067cbd07d7b3df21a0f2d5cedfe3d822"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a067cbd07d7b3df21a0f2d5cedfe3d822"></a>
<a class="el" href="group__Util.html#gaccfeb6b1e8cf41731fde610549bee67c">real_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classOFELI_1_1Tetra4.html#a067cbd07d7b3df21a0f2d5cedfe3d822">getVolume</a> () const </td></tr>
<tr class="memdesc:a067cbd07d7b3df21a0f2d5cedfe3d822"><td class="mdescLeft">&#160;</td><td class="mdescRight">Return volume of element. <br /></td></tr>
<tr class="separator:a067cbd07d7b3df21a0f2d5cedfe3d822"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ace27ff0c36dcb1c625beaa1660804eb7"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="ace27ff0c36dcb1c625beaa1660804eb7"></a>
<a class="el" href="structOFELI_1_1Point.html">Point</a>&lt; <a class="el" href="group__Util.html#gaccfeb6b1e8cf41731fde610549bee67c">real_t</a> &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classOFELI_1_1Tetra4.html#ace27ff0c36dcb1c625beaa1660804eb7">getRefCoord</a> (const <a class="el" href="structOFELI_1_1Point.html">Point</a>&lt; <a class="el" href="group__Util.html#gaccfeb6b1e8cf41731fde610549bee67c">real_t</a> &gt; &amp;x) const </td></tr>
<tr class="memdesc:ace27ff0c36dcb1c625beaa1660804eb7"><td class="mdescLeft">&#160;</td><td class="mdescRight">Return reference coordinates of a point <code>x</code> in element. <br /></td></tr>
<tr class="separator:ace27ff0c36dcb1c625beaa1660804eb7"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a497b1ac36e44c874a349867507206f25"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a497b1ac36e44c874a349867507206f25"></a>
bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classOFELI_1_1Tetra4.html#a497b1ac36e44c874a349867507206f25">isIn</a> (const <a class="el" href="structOFELI_1_1Point.html">Point</a>&lt; <a class="el" href="group__Util.html#gaccfeb6b1e8cf41731fde610549bee67c">real_t</a> &gt; &amp;x)</td></tr>
<tr class="memdesc:a497b1ac36e44c874a349867507206f25"><td class="mdescLeft">&#160;</td><td class="mdescRight">Check whether point <code>x</code> is in current tetrahedron or not. <br /></td></tr>
<tr class="separator:a497b1ac36e44c874a349867507206f25"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aef402685d6ed44658eb81625bd9e4cd2"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="aef402685d6ed44658eb81625bd9e4cd2"></a>
<a class="el" href="group__Util.html#gaccfeb6b1e8cf41731fde610549bee67c">real_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classOFELI_1_1Tetra4.html#aef402685d6ed44658eb81625bd9e4cd2">getInterpolate</a> (const <a class="el" href="structOFELI_1_1Point.html">Point</a>&lt; <a class="el" href="group__Util.html#gaccfeb6b1e8cf41731fde610549bee67c">real_t</a> &gt; &amp;x, const <a class="el" href="classOFELI_1_1LocalVect.html">LocalVect</a>&lt; <a class="el" href="group__Util.html#gaccfeb6b1e8cf41731fde610549bee67c">real_t</a>, 4 &gt; &amp;v)</td></tr>
<tr class="memdesc:aef402685d6ed44658eb81625bd9e4cd2"><td class="mdescLeft">&#160;</td><td class="mdescRight">Return interpolated value at point of coordinate <code>x</code> <br /></td></tr>
<tr class="separator:aef402685d6ed44658eb81625bd9e4cd2"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:af951f990a89682795f761214c6384304"><td class="memItemLeft" align="right" valign="top"><a class="el" href="structOFELI_1_1Point.html">Point</a>&lt; <a class="el" href="group__Util.html#gaccfeb6b1e8cf41731fde610549bee67c">real_t</a> &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classOFELI_1_1Tetra4.html#af951f990a89682795f761214c6384304">EdgeSh</a> (size_t k, <a class="el" href="structOFELI_1_1Point.html">Point</a>&lt; <a class="el" href="group__Util.html#gaccfeb6b1e8cf41731fde610549bee67c">real_t</a> &gt; s)</td></tr>
<tr class="memdesc:af951f990a89682795f761214c6384304"><td class="mdescLeft">&#160;</td><td class="mdescRight">Return edge shape function.  <a href="#af951f990a89682795f761214c6384304">More...</a><br /></td></tr>
<tr class="separator:af951f990a89682795f761214c6384304"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a9415e45963eabefa9d1d8ad25c774091"><td class="memItemLeft" align="right" valign="top"><a class="el" href="structOFELI_1_1Point.html">Point</a>&lt; <a class="el" href="group__Util.html#gaccfeb6b1e8cf41731fde610549bee67c">real_t</a> &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classOFELI_1_1Tetra4.html#a9415e45963eabefa9d1d8ad25c774091">CurlEdgeSh</a> (size_t k)</td></tr>
<tr class="memdesc:a9415e45963eabefa9d1d8ad25c774091"><td class="mdescLeft">&#160;</td><td class="mdescRight">Return curl of edge shape function.  <a href="#a9415e45963eabefa9d1d8ad25c774091">More...</a><br /></td></tr>
<tr class="separator:a9415e45963eabefa9d1d8ad25c774091"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aef875a901767a614557a4aca5e6d08f9"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="aef875a901767a614557a4aca5e6d08f9"></a>
<a class="el" href="group__Util.html#gaccfeb6b1e8cf41731fde610549bee67c">real_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classOFELI_1_1Tetra4.html#aef875a901767a614557a4aca5e6d08f9">getMaxEdgeLength</a> () const </td></tr>
<tr class="memdesc:aef875a901767a614557a4aca5e6d08f9"><td class="mdescLeft">&#160;</td><td class="mdescRight">Return maximal edge length of tetrahedron. <br /></td></tr>
<tr class="separator:aef875a901767a614557a4aca5e6d08f9"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a9b14e7e0ca32bd24f27519ed8ed0d0c8"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a9b14e7e0ca32bd24f27519ed8ed0d0c8"></a>
<a class="el" href="group__Util.html#gaccfeb6b1e8cf41731fde610549bee67c">real_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classOFELI_1_1Tetra4.html#a9b14e7e0ca32bd24f27519ed8ed0d0c8">getMinEdgeLength</a> () const </td></tr>
<tr class="memdesc:a9b14e7e0ca32bd24f27519ed8ed0d0c8"><td class="mdescLeft">&#160;</td><td class="mdescRight">Return minimal edge length of tetrahedron. <br /></td></tr>
<tr class="separator:a9b14e7e0ca32bd24f27519ed8ed0d0c8"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aa7d706a44a4e55358fd7941724ef55b7"><td class="memItemLeft" align="right" valign="top">std::vector&lt; <a class="el" href="structOFELI_1_1Point.html">Point</a>&lt; <a class="el" href="group__Util.html#gaccfeb6b1e8cf41731fde610549bee67c">real_t</a> &gt; &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classOFELI_1_1Tetra4.html#aa7d706a44a4e55358fd7941724ef55b7">DSh</a> () const </td></tr>
<tr class="memdesc:aa7d706a44a4e55358fd7941724ef55b7"><td class="mdescLeft">&#160;</td><td class="mdescRight">Calculate partial derivatives of shape functions at element nodes.  <a href="#aa7d706a44a4e55358fd7941724ef55b7">More...</a><br /></td></tr>
<tr class="separator:aa7d706a44a4e55358fd7941724ef55b7"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:abf13023b750b4a215814cfb805b145da"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="abf13023b750b4a215814cfb805b145da"></a>
<a class="el" href="group__Util.html#gaccfeb6b1e8cf41731fde610549bee67c">real_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classOFELI_1_1FEShape.html#abf13023b750b4a215814cfb805b145da">Sh</a> (size_t i) const </td></tr>
<tr class="memdesc:abf13023b750b4a215814cfb805b145da"><td class="mdescLeft">&#160;</td><td class="mdescRight">Return shape function of node <code>i</code> at given point. <br /></td></tr>
<tr class="separator:abf13023b750b4a215814cfb805b145da"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a0f35cc59cf2218efd06b13c2487f31cc"><td class="memItemLeft" align="right" valign="top"><a class="el" href="group__Util.html#gaccfeb6b1e8cf41731fde610549bee67c">real_t</a>&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classOFELI_1_1FEShape.html#a0f35cc59cf2218efd06b13c2487f31cc">getDet</a> () const </td></tr>
<tr class="memdesc:a0f35cc59cf2218efd06b13c2487f31cc"><td class="mdescLeft">&#160;</td><td class="mdescRight">Return determinant of jacobian.  <a href="#a0f35cc59cf2218efd06b13c2487f31cc">More...</a><br /></td></tr>
<tr class="separator:a0f35cc59cf2218efd06b13c2487f31cc"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a802168de29d5e265ee01a57fd98793e8"><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a802168de29d5e265ee01a57fd98793e8"></a>
<a class="el" href="structOFELI_1_1Point.html">Point</a>&lt; <a class="el" href="group__Util.html#gaccfeb6b1e8cf41731fde610549bee67c">real_t</a> &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classOFELI_1_1FEShape.html#a802168de29d5e265ee01a57fd98793e8">getCenter</a> () const </td></tr>
<tr class="memdesc:a802168de29d5e265ee01a57fd98793e8"><td class="mdescLeft">&#160;</td><td class="mdescRight">Return coordinates of center of element. <br /></td></tr>
<tr class="separator:a802168de29d5e265ee01a57fd98793e8"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ad5af4f17aea53c0ab1e8ce2494f23234"><td class="memItemLeft" align="right" valign="top"><a class="el" href="structOFELI_1_1Point.html">Point</a>&lt; <a class="el" href="group__Util.html#gaccfeb6b1e8cf41731fde610549bee67c">real_t</a> &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classOFELI_1_1FEShape.html#ad5af4f17aea53c0ab1e8ce2494f23234">getLocalPoint</a> () const </td></tr>
<tr class="memdesc:ad5af4f17aea53c0ab1e8ce2494f23234"><td class="mdescLeft">&#160;</td><td class="mdescRight">Localize a point in the element.  <a href="#ad5af4f17aea53c0ab1e8ce2494f23234">More...</a><br /></td></tr>
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<tr class="memitem:a565411b0254679f383549c1a09bf2352"><td class="memItemLeft" align="right" valign="top"><a class="el" href="structOFELI_1_1Point.html">Point</a>&lt; <a class="el" href="group__Util.html#gaccfeb6b1e8cf41731fde610549bee67c">real_t</a> &gt;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classOFELI_1_1FEShape.html#a565411b0254679f383549c1a09bf2352">getLocalPoint</a> (const <a class="el" href="structOFELI_1_1Point.html">Point</a>&lt; <a class="el" href="group__Util.html#gaccfeb6b1e8cf41731fde610549bee67c">real_t</a> &gt; &amp;s) const </td></tr>
<tr class="memdesc:a565411b0254679f383549c1a09bf2352"><td class="mdescLeft">&#160;</td><td class="mdescRight">Localize a point in the element.  <a href="#a565411b0254679f383549c1a09bf2352">More...</a><br /></td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Defines a three-dimensional 4-node tetrahedral finite element using <code>P<sub>1</sub></code> interpolation. </p>
<p>The reference element is the right tetrahedron with four unit edges interpolation.</p>
<dl class="section author"><dt>Author</dt><dd>Rachid Touzani </dd></dl>
<dl class="section copyright"><dt>Copyright</dt><dd>GNU Lesser Public License </dd></dl>
</div><h2 class="groupheader">Member Function Documentation</h2>
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          <td class="memname"><a class="el" href="group__Util.html#gaccfeb6b1e8cf41731fde610549bee67c">real_t</a> Sh </td>
          <td>(</td>
          <td class="paramtype">size_t&#160;</td>
          <td class="paramname"><em>i</em>, </td>
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          <td class="paramtype"><a class="el" href="structOFELI_1_1Point.html">Point</a>&lt; <a class="el" href="group__Util.html#gaccfeb6b1e8cf41731fde610549bee67c">real_t</a> &gt;&#160;</td>
          <td class="paramname"><em>s</em>&#160;</td>
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<p>Calculate shape function of node <code>i</code> at a given point <code>s</code>. </p>
<p><code>s</code> is a point in the reference tetrahedron. </p>

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          <td class="paramname"><em>s</em>&#160;</td>
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<p>Return edge shape function. </p>
<dl class="params"><dt>Parameters</dt><dd>
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    <tr><td class="paramdir">[in]</td><td class="paramname">k</td><td>Local edge number for which the edge shape function is computed </td></tr>
    <tr><td class="paramdir">[in]</td><td class="paramname">s</td><td>Local coordinates in element </td></tr>
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<dl class="section remark"><dt>Remarks</dt><dd><a class="el" href="classOFELI_1_1Element.html" title="To store and treat finite element geometric information. ">Element</a> edges are ordered as follows: <a class="el" href="classOFELI_1_1Edge.html" title="To describe an edge. ">Edge</a> <code>k</code> has end vertices <code>k</code> and <code>k+1</code> </dd></dl>

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<p>Return curl of edge shape function. </p>
<dl class="params"><dt>Parameters</dt><dd>
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    <tr><td class="paramdir">[in]</td><td class="paramname">k</td><td>Local edge number for which the curl of the edge shape function is computed </td></tr>
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<dl class="section remark"><dt>Remarks</dt><dd><a class="el" href="classOFELI_1_1Element.html" title="To store and treat finite element geometric information. ">Element</a> edges are ordered as follows: <a class="el" href="classOFELI_1_1Edge.html" title="To describe an edge. ">Edge</a> <code>k</code> has end vertices <code>k</code> and <code>k+1</code> </dd></dl>

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          <td class="memname">std::vector&lt;<a class="el" href="structOFELI_1_1Point.html">Point</a>&lt;<a class="el" href="group__Util.html#gaccfeb6b1e8cf41731fde610549bee67c">real_t</a>&gt; &gt; DSh </td>
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<p>Calculate partial derivatives of shape functions at element nodes. </p>
<dl class="section return"><dt>Returns</dt><dd>Vector of partial derivatives of shape functions <em>e.g.</em> <code>dsh</code>[i-1].x, <code>dsh</code>[i-1].y, are partial derivatives of the <em>i</em>-th shape function </dd></dl>

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<p>Return determinant of jacobian. </p>
<p>If the transformation (Reference element -&gt; Actual element) is not affine, member function <b>setLocal()</b> must have been called before in order to calcuate relevant quantities. </p>

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<p>Localize a point in the element. </p>
<p>Return actual coordinates in the reference element. If the transformation (Reference element -&gt; Actual element) is not affine, member function <b>setLocal()</b> must have been called before in order to calcuate relevant quantities. </p>

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          <td>(</td>
          <td class="paramtype">const <a class="el" href="structOFELI_1_1Point.html">Point</a>&lt; <a class="el" href="group__Util.html#gaccfeb6b1e8cf41731fde610549bee67c">real_t</a> &gt; &amp;&#160;</td>
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<p>Localize a point in the element. </p>
<p>Return actual coordinates where <code>s</code> are coordinates in the reference element. </p>

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